Equivariant Differential Cohomology
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Submission date: 25. Oct. 2015
published in: Transactions of the American Mathematical Society, 370 (2018) 11, p. 8237-8283
DOI number (of the published article): 10.1090/tran/7315
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The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action on the manifold: The definition of equivariant characteristic forms in the Cartan model due to [BerlineVergne] motivates a refinement of equivariant integral cohomology by all Cartan cocycles. In view of this, we will also review previous definitions critically, in particular the one given in [Gomi].